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The question is from the relative speed . It is a straightforward question and tests the understanding of the concepts. Time Speed and Distance is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 24: Two persons A and B start moving at each other from point P and Q respectively which are 1400 Km apart. Speed of A is 50 Km/hr and that of B is 20 Km/hr. How far is A from Q when he meets B for the 22nd time?

  1. 1000 km
  2. 400 km
  3. 800 km
  4. 1400 km

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Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: We can solve this by finding the total distance covered by them.

Total distance travelled by both of them for 22nd meeting = 1400 + (21 * 2 * 1400) = 43 * 1400
Distance travelled by each will be in proportion of their speed :
Therefore, distance travelled by A = 50/(50 + 20) * 43 * 1400 = 43000 (Note - Always do complicated calculations at last because things cancel out generally)
Now, for every odd multiple of 1400, A will be at Q and for every even multiple of 1400 A will be at P. So, at 42000 Km (1400 x 30, even multiple) A will beat P. So at their 22 meeting, A will be 1000 Km from P, therefore, 400 Km from Q.

The question is "How far is A from Q when he meets B for the 22nd time?"

Hence, the answer is 400 km

Choice B is the correct answer.

 


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